Christoph Clavius · 1611
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Tomus I of Clavius’s collected mathematical works gathers his geometry and trigonometry. Its core is his celebrated commentary on Euclid’s Elements (Books I–XV, with a sixteenth added) — the standard Renaissance Euclid, dense with labelled construction diagrams and scholia.
Before reaching Euclid, Clavius sets out prolegomena to the mathematical disciplines as a whole: why they are called what they are, how they divide, who invented them, wherein their nobility and excellence lie, and what they are good for. He then defines the working vocabulary — what mathematicians mean by a problem, a theorem, a proposition, a lemma, and by the principles of a science. Only then does he commend Euclid, divide the Elements, and begin.
The Euclid commentary proceeds definition by definition and proposition by proposition, and the volume flags what Clavius himself added to the edition. After it come his commentary on Theodosius’s Sphaerica, the geometry of the sphere, and a treatise on the doctrine of sines, tangents and secants with the theory of plane and spherical triangles, accompanied by extensive numeric trigonometric tables.
This is the volume the other four stand on. Renaissance astronomy is spherical trigonometry applied to the heavens, and Clavius supplies both halves here — the geometry, in the edition of Euclid that a European student was most likely to learn from, and the trigonometric machinery with the tables needed to compute with it. His Euclid was not merely a reprint: the commentary and scholia are substantial enough that “Clavius’s Euclid” became a book in its own right, and he was known in his own century as the Euclid of his age.
The translated source is the Mainz printing of 1611, the year before Clavius’s death, opening with an engraved title page, a dedicatory epistle to Prince Johann Gottfried, and a general index to all the volumes of the collected works.